Remarks on the Bourgain-Brezis-Mironescu Approach to Sobolev Spaces

B. Bojarski

B. Bojarski

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011), p. 65-75 / Harvested from The Polish Digital Mathematics Library

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Résumé

For a function $f \in L_{l o c}^{p} (ℝ ⁿ)$ the notion of p-mean variation of order 1, $₁^{p} (f, ℝ ⁿ)$ is defined. It generalizes the concept of F. Riesz variation of functions on the real line ℝ¹ to ℝⁿ, n > 1. The characterisation of the Sobolev space $W^{1, p} (ℝ ⁿ)$ in terms of $₁^{p} (f, ℝ ⁿ)$ is directly related to the characterisation of $W^{1, p} (ℝ ⁿ)$ by Lipschitz type pointwise inequalities of Bojarski, Hajłasz and Strzelecki and to the Bourgain-Brezis-Mironescu approach.

Publié le : 2011-01-01

Zbl 1230.46028

EUDML-ID : urn:eudml:doc:286291

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     title = {Remarks on the Bourgain-Brezis-Mironescu Approach to Sobolev Spaces},
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     year = {2011},
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B. Bojarski. Remarks on the Bourgain-Brezis-Mironescu Approach to Sobolev Spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 65-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-1-8/